GATE Mechanical Engineering Materials, Manufacturing and Industrial Engineering Syllabus

For the Hollomon power law, at what true strain does necking begin in a tensile test?

Necking (instability) begins when $\varepsilon_{T} = n$, the strain-hardening exponent.

What does the area under the stress-strain curve represent?

Total area = toughness (energy absorbed per unit volume to fracture); area up to the elastic limit = modulus of resilience, $U_r = \frac{\sigma_y^{2}}{2E}$.

List the four main casting process categories with one example each.

Expendable mold (sand casting, investment casting), permanent mold (gravity die casting), pressure die casting (hot/cold chamber), and centrifugal casting.

What is investment (lost-wax) casting and one key advantage?

A wax pattern is coated with a ceramic shell, then melted out, and metal is poured into the cavity. Advantage: high dimensional accuracy and excellent surface finish for intricate shapes.

What is the purpose of a core in sand casting?

A core (usually sand) forms internal cavities, holes, or undercuts in a casting that cannot be produced by the main mold halves.

List the main pattern allowances used in pattern design.

Shrinkage allowance, machining (finish) allowance, draft (taper) allowance, distortion (camber) allowance, and shake (rapping) allowance.

Why is shrinkage allowance provided on a pattern, and what kinds of shrinkage occur?

To compensate for solid (and liquid/solidification) contraction so the cast part reaches the correct final dimensions. Shrinkage occurs in three stages: liquid contraction, solidification contraction, and solid-state contraction.

State Chvorinov's rule for solidification time of a casting.

$t_{s} = B\left(\dfrac{V}{A}\right)^{n}$, where $V$ is volume, $A$ is surface area, $B$ is the mold constant and $n \approx 2$. Larger $V/A$ ratio means slower solidification.

What is a riser (feeder) and the design rule relating its solidification time to the casting?

A riser is a reservoir supplying liquid metal to compensate for shrinkage during solidification. It must solidify after the casting: $\left(\frac{V}{A}\right)_{riser} > \left(\frac{V}{A}\right)_{casting}$ (Chvorinov rule).

What is directional solidification and why is it desirable?

Controlled solidification progressing from the thinnest/farthest section toward the riser so the riser solidifies last, ensuring continuous feeding and preventing shrinkage porosity in the casting.

State Caine's relation / the concept of freezing ratio in riser design.

Caine's equation: $X = \dfrac{a}{Y - b} + c$, where $X$ is the freezing ratio $\frac{(A/V)_{casting}}{(A/V)_{riser}}$ and $Y$ is the riser/casting volume ratio; it sets the minimum riser size to avoid shrinkage.

Define the gating ratio in a gating system.

Gating ratio = sprue area : runner area : ingate area (e.g. $1:2:2$). It classifies the system as pressurized ($\geq$) or unpressurized ($\leq$, gates largest) based on where the smallest cross-section is.

Using Bernoulli/Torricelli, what is the velocity of metal at the base of a sprue of effective head $h$?

$v = \sqrt{2 g h}$, where $h$ is the metallostatic head and $g$ is gravitational acceleration.

Why is a sprue tapered (smaller at the bottom)?

To match the natural acceleration of falling metal ($v = \sqrt{2gh}$); by continuity the stream narrows as it descends, so tapering prevents air aspiration and turbulence.

Differentiate plastic deformation in terms of slip and twinning.

Slip: planes of atoms glide over one another along slip systems (dominant, large deformation). Twinning: a region reorients to form a mirror image across a twin plane (small, sudden, common in HCP/BCC at high strain rate).

State the von Mises (distortion energy) yield criterion in terms of principal stresses.

Yielding occurs when $\frac{1}{\sqrt{2}}\sqrt{(\sigma_1-\sigma_2)^2 + (\sigma_2-\sigma_3)^2 + (\sigma_3-\sigma_1)^2} = \sigma_y$.

State the Tresca (maximum shear stress) yield criterion.

Yielding occurs when the maximum shear stress reaches $\frac{\sigma_y}{2}$: $\sigma_{max} - \sigma_{min} = \sigma_y$ (difference of largest and smallest principal stresses equals yield strength).

In pure shear, what yield shear stress do Tresca and von Mises predict relative to $\sigma_y$?

Tresca: $\tau_y = 0.5\,\sigma_y$. Von Mises: $\tau_y = \frac{\sigma_y}{\sqrt{3}} = 0.577\,\sigma_y$. Von Mises predicts the higher value.

Define hot working and cold working with respect to the recrystallization temperature.

Hot working: deformation above the recrystallization temperature (no strain hardening, lower forces). Cold working: deformation below recrystallization temperature (strain hardening, better finish and tolerances).

Give the approximate recrystallization temperature as a fraction of the melting temperature.

$T_{recryst} \approx (0.3\text{ to } 0.5)\,T_{m}$, with $T_m$ in absolute (Kelvin) temperature.

List the four primary bulk deformation processes.

Forging, rolling, extrusion, and drawing (wire/rod/tube drawing).

For open-die forging of a cylinder, how does friction affect the required force?

Friction at the die-workpiece interface causes a friction hill (pressure rises toward the center), increasing the average pressure and forging force: $F = p_{avg} A$ with $p_{avg} > \sigma_y$.

In flat rolling, write the expression for true strain and the draft.

Draft $d = h_0 - h_f$ (reduction in thickness). True (height) strain $\varepsilon = \ln\!\left(\dfrac{h_0}{h_f}\right)$, where $h_0$ and $h_f$ are entry and exit thicknesses.

What is the maximum draft possible in rolling in terms of roll radius and friction?

$d_{max} = \mu^{2} R$, where $\mu$ is the coefficient of friction and $R$ is the roll radius; the bite condition requires $\tan\alpha \leq \mu$.

Define the neutral (no-slip) point in rolling.

The point along the arc of contact where the strip and roll surface velocities are equal; before it the roll moves faster than the strip, after it the strip moves faster than the roll, reversing friction direction.

Differentiate direct and indirect extrusion.

Direct (forward): ram and metal flow in the same direction; high friction along the container wall. Indirect (backward): die moves toward the billet (or billet stays still while hollow ram pushes die), so metal flows opposite to ram motion; lower friction and force.

Write the extrusion ratio and the ideal extrusion pressure relation.

Extrusion ratio $R = \dfrac{A_0}{A_f}$. Ideal pressure $p = \bar{\sigma}\,\ln R$, where $\bar{\sigma}$ is the mean flow stress; actual pressure is higher due to friction and redundant work.

In wire/rod drawing, write the maximum reduction per pass for a perfectly plastic, frictionless material.

The drawing stress cannot exceed the flow stress, giving $\ln\!\left(\dfrac{A_0}{A_f}\right) \leq 1$, i.e. maximum area reduction per pass is $1 - \frac{1}{e} \approx 63\%$.

In sheet metal shearing, write the shearing force in terms of sheet thickness, cut length and shear strength.

$F = \tau \cdot t \cdot L$, where $\tau$ is the ultimate shear strength, $t$ is sheet thickness, and $L$ is the total length of the sheared edge.

Differentiate blanking and piercing (punching).

In blanking the punched-out piece is the product (slug is the part). In piercing/punching the punched-out slug is scrap and the remaining sheet with the hole is the product.

Define the limiting drawing ratio (LDR) in deep drawing.

$LDR = \dfrac{D_{max}}{d_p}$, the maximum ratio of blank diameter to punch (cup) diameter that can be drawn in one pass without tearing; typically $\approx 1.8$–$2.0$.

What is the role of the blank holder in deep drawing?

It applies pressure to hold the blank flange against the die, preventing wrinkling due to circumferential compressive stresses while allowing the metal to draw radially inward into the die cavity.